Classifying Triangles Calculator

Triangles can be classified in two complementary ways: by comparing their side lengths and by comparing their interior angles. A side classification says whether all, two, or none of the sides are equal. An angle classification says whether the largest angle is less than, equal to, or greater than 90 degrees. Together, these names provide a compact but precise description, such as an acute isosceles triangle or a right scalene triangle. An equilateral triangle has three equal sides. Its three angles are also equal, so each measures 60 degrees and every equilateral triangle is acute. An isosceles triangle has at least two equal sides and therefore at least two equal angles. A scalene triangle has three unequal sides and three unequal angles. The calculator compares side values with a small numerical tolerance so normal decimal input is not misclassified because of floating-point representation. The angle type can be found without calculating inverse trigonometric functions. First arrange the sides so that c is the longest. Compare c squared with a squared plus b squared. Equality is the Pythagorean relationship and identifies a right triangle. If c squared is smaller, the largest angle is less than 90 degrees and the triangle is acute. If c squared is larger, the largest angle exceeds 90 degrees and the triangle is obtuse. This converse of the Pythagorean theorem is fast and reliable. Before classification, the triangle inequality must hold. The sum of the two shorter lengths must be strictly greater than the longest length. Equality would produce a flattened, degenerate figure with zero area, while a smaller sum means the endpoints cannot meet at all. The tool also rejects zero and negative lengths because geometric side lengths must be positive. Units do not affect classification as long as all three entries use the same unit. Multiplying every side by a common scale factor produces a similar triangle with the same labels. This makes the calculator useful for geometry homework, construction checks, coordinate-distance results, drafting, and mathematical demonstrations. It reports both classification systems at once, helping you verify sketches and recognize theorems that apply to the triangle before performing area, height, or trigonometric calculations.